I know when two metals are in contact, the Fermi level must line up, somewhere between the two original metals for thermodynamic equilibrium.
When this happens, I wonder how much does the Fermi level change.
For example, what would the Fermi level be if 1 mole of copper and 1 mole of lithium are in contact at $T = 0\ {\rm K}$ (or finite $T$) ?
I'm guessing if the same quantity of two different metals are in contact, the Fermi level would exactly be in the center of the two metals, which is $$\frac{ 7(\rm copper) + 4.74(\rm lithium) } { 2} = 5.87\ {\rm eV},$$ but I'm not sure. Is this right?
The reason why I'm asking this question is related to voltage measurement with a voltmeter.
For example, for voltage measurement of a battery, if material of one probe wire is different from the other, would the measured voltage be different compared to the voltage measured when both probe wires are the same material? (in perspective of fundamental)
I would like to know universal method for calculation of Fermi level change when metal-metal junction happens.
